Bangalore Probability Seminar: Number of components of polynomial lemniscates: deterministic and random
Speaker 
Koushik Ramachandran ( TIFR CAM, Bangalore)


When 
Apr 08, 2024
from 02:00 PM to 03:00 PM 
Where  LH011 ( TIFR CAM ) Hybrid 
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Title
Number of components of polynomial lemniscates: deterministic and random
Abstract
A polynomial lemniscate is a set of the form \{z: p(z) < 1\}, where p is a complex polynomial. How many connected components does a lemniscate have? In general it can be as large as the degree deg(p). What happens if the zeros are constrained to lie on a fixed compact set in the plane? This is a classical question that goes back to Erdos, Herzog, and Piranian from the 1950's. In these talks we will deal with the component count for both deterministic and random lemniscates. The first lecture will provide some background and motivation for the results, particularly emphasizing the interplay of potential theory and probability. The second lecture will deal with the average number of connected components for random polynomials whose zeros are sampled i.i.d. from certain distributions in the closed unit disk.
Zoom link: https://us02web.zoom.us/j/88670406480
Meeting ID: 886 7040 6480